In electronic systems it is often desirable to reduce the physical volume or area required to implement a given signal processing function. An example is a lens-based antenna beamformer. The area required in a beamforming lens can be dozens to hundreds of square wavelengths depending on the antenna array size and number of beam ports. To reduce the physical size of a beamforming lens without sacrificing its electrical dimensions, the electromagnetic propagation velocity within the lens must be slowed relative to the speed of light in free space. Antenna designers have historically used various dielectric materials to fill parallel plate waveguides used as lenses. [See for example D. H. Archer et. al, U.S. Pat. No. 3,761,936, and E. O. Rauch, European Microwave Conference, 1992, pp. 876-881.] The relative permittivity is that of the host dielectric, which is often lower than about 6. This limits the potential size reduction to a factor of 6 in area, or √{square root over (6)} in linear dimensions. Conventional high dielectric materials are often too lossy, especially at high microwave and millimeterwave frequencies.
When using homogeneous microwave laminates the relative permittivity does not vary as a function of position or as a function of the direction of wave propagation within a waveguide that employs such a material. There are examples of inhomogeneous dielectric materials formed by drilling patterns of air-filled holes in an otherwise homogeneous dielectric slab [A. Petosa et. al., IEEE Antennas and Propagation Intl. Symposium, Monterey, Calif., June 2004, pp. 1106-1109, and L. Schulwitz, et. al, IEEE Trans. on Microwave Theory and Techniques, Vol. 56, No. 12, December 2008, pp. 2734-2741]. But, this method of engineering an inhomogeneous dielectric medium results in a decrease of the permittivity relative to the host dielectric.
Solid dielectric materials associated with microwave components formed using PPW or stripline also increase the weight or mass of the component. Conventional dielectric materials such as high-quality microwave laminates are usually manufactured separately as sheets and are typically clad with metal. Using such dielectric materials in higher-level assemblies may require etching, plating, drilling, bonding, soldering, and possibly other manufacturing operations. Very tight manufacturing tolerances are required for microwave and millimeterwave assemblies and packages that use conventional dielectric sheets. For antenna beamformer applications, the wave impedance of an absorptive structure used as a lens wall should be matched with the wave impedance of an interior region of the lens beamformer. This implies the need to match the ratio of effective permeability to effective permittivity on both sides of the wall interface.